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a fruit seller sold 121 fruits in the morning and 1/4 of the remaining fruits in the afternoon. If he had 1/5 of the total number fruits left, how many fruits did he have at first?

Feb 3, 2018

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OK.......

Call the total number of fruits started with, F

So......

After  the seller sells   121 fruits... he has  F - 121 reamaining

And he sells  (1/ 4)  of these in the afternoon =(1/4)(F - 121)

So.....what he/she strated with  - what was  sold in the morning - what was sold in the afternoon = (1/5)F

So....we have this equation

F  -  121  -  (1/4)(F - 121)  =  (1/5)F      simplify

F - 121  - (1/4)F +   121/4 =  (1/5)F

(3/4)F - 121 +  121/4  = (1/5)F

(3/4)F  -  484/4 + 121/4  =  (1/5)F

(3/4)F - 363/4  = (1/5)F       subtract   (1/5)F from both sides..add 363/4 to both sides

(3/4)F - (1/5)F   =  363/4      get a common denominator on the right

(15/20) - (4/20) F  =  363/4

(11/20)F  =  363/4        multiply both sides by   (20/11)

F   =  (363/4) (20/11)  =   (363/11) (20/4)   =  (33)(5)   =   165 fruits

Proof

165  - 121  =     44 left  after the morning

(1/4) of these sold in the afternoon  =  11 sold   and 33 remain......and this is (1/5) of the total   Feb 3, 2018